To build endurance, I do sessions of about 25-30 routes (well below my onsight limit of course, many as laps on top-rope). If you do that 3x week for a couple of months, you shouldn't get nearly as pumped as you do now.

It's supposed to be so that gravity can drain some of the blood and lactic acid from your arms before you shake below to allow fresh blood back in. That's the theory, in practice the difference may only be slight (or only psychological) but I often give it a go out of habit when mega pumped.